Best Known (8, 8+21, s)-Nets in Base 64
(8, 8+21, 177)-Net over F64 — Constructive and digital
Digital (8, 29, 177)-net over F64, using
- t-expansion [i] based on digital (7, 29, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
(8, 8+21, 257)-Net in Base 64 — Constructive
(8, 29, 257)-net in base 64, using
- 3 times m-reduction [i] based on (8, 32, 257)-net in base 64, using
- base change [i] based on digital (0, 24, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 24, 257)-net over F256, using
(8, 8+21, 8197)-Net in Base 64 — Upper bound on s
There is no (8, 29, 8198)-net in base 64, because
- 1 times m-reduction [i] would yield (8, 28, 8198)-net in base 64, but
- the generalized Rao bound for nets shows that 64m ≥ 374 273070 898052 327941 254869 202352 815192 340489 148416 > 6428 [i]